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uously as a preponderance of hydrogen in the present-day universe, arose from a competition between the cosmic expansion and nuclear and subnuclear reactions. The origin of structural order is more controversial. I will argue that it might have been produced by a bottom-up process of gravitational clustering. For references, see [44, 45, 46J. See also, [69J.

On sequential compression with distortion

Abraham Lempel, HP Israel Science Centre lempel@hpl.hp.com

Abstract not available.

Large Deviations, Statistical Mechanics and Information Theory

John Lewis, Dublin Institute for Advanced Studies lewis@stp.dias.ie

In 1965, Ruelle showed how to give a precise meaning to Boltzmann's Formula. Exploring the consequences of Ruelle's definition leads to the theory of large deviations and information theory. For a reference, see [48J.

(Editor's note: John Lewis also gave an additional tutorial lecture on large deviations. Among the texts he cited were [15, 29J.)

Entropy in States of the Self-Excited System with External Forcing

Grzegorz Litak, University of Lublin glitak@archimedes.pol.lublin.pl

Self-excited systems with external driving force are characterized by a number of interesting features as synchronization of vibration, and transition to chaos. Using an one dimensional example of the self-excited system-Froude pendulum we examined the influence of parameters on the system itegrity. The motion is described by the following nonlinear equation with Raylaigh damping term

¢- (0: - f31})¢ + 1'sin(¢» = B coswt

There are two characteristic frequencies in the system: p - self-excited and w - driving fre quency. For the nodal driving force amplitude B the system oscillates with self-excited fre quency. For B :f: 0, depending on the system parameters, two cases of regular solutions may occurred: mono-frequency solution and the quasi-periodic solution with the modulated am plitude. Except for regular solution the chaotic one appear. The chaotic vibrations correspond with the positive value of Kolmogorov Entropy K. Here the entropy is the measure of chaotic ity of the system, indicating how fast the information about the dymamical system state is losing. The definition of Kolmogorov entropy is in analogy with Shannon's in information the ory. In our paper the Kolmogorov entropy and other indicators of the dynamical system states

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